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The quantity \(mr^2\) is called the rotational inertia or moment of inertia of a point mass \(m\) a distance \(r\) from the center of rotation. Figure \(\PageIndex{2}\): An object is supported by a horizontal frictionless table and is attached to a pivot point by a cord that supplies centripetal force.
- Rotational Kinetic Energy
Example \(\PageIndex{1}\): Calculating the Work and Energy...
- Kinematics of Rotational Motion
This example illustrates that relationships among rotational...
- 5.3: Rotational Inertia
Calculating Rotational Inertia for Continuous Objects. Our...
- 5.2: Rotational Inertia
Calculating Rotational Inertia for Continuous Objects. Our...
- Rotational Kinetic Energy
When you are done with all of this, you oftentimes end up with a nice little formula that looks something like this… I = α mr 2 where α is a simple rational number like 1 for a hoop, ½ for a cylinder, or ⅖ for a sphere.
2 sie 2023 · Moment of inertia, also known as rotational inertia or angular mass, is a physical quantity that resists a rigid body’s rotational motion. It is analogous to mass in translational motion. It determines the torque required to rotate an object by a given angular acceleration.
Calculating Rotational Inertia for Continuous Objects. Our task is to compute the rotational inertia, for which the formula in terms of masses and their positions is different from the one for center of mass (see Section 4.2), but the procedure is exactly the same.
The formula v = r is true for a wheel spinning about a fixed axis, where v is speed of points on rim. A similar formulas v CM = r works for a wheel rolling on the ground. Two very different situations, different v’s: v = speed of rim vs. v cm = speed of axis. But v = r true for both.
Apply net τ = Iα, α = net τ I net τ = Iα, α = net τ I, the rotational equivalent of Newton’s second law, to solve the problem. Care must be taken to use the correct moment of inertia and to consider the torque about the point of rotation. As always, check the solution to see if it is reasonable.
21 maj 2023 · Calculating Rotational Inertia for Continuous Objects. Our task is to compute the rotational inertia, for which the formula in terms of masses and their positions is different from the one for center of mass (see Section 4.2), but the procedure is exactly the same.
